Group #15676690 — subgroups

Subgroups — #15676690

Order 2944.

504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₄₆	C₂	1	2	yes	maximal
2	#13092349	C₂	1	4	yes	maximal
3	#13092338	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₂₃	C₂	1	4	yes	maximal
5	C₂₃×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₆	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₂₃	C₂²	1	8	yes	—
11	C₂×Dic₂₃⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄×Dic₂₃	C₂²	1	4	yes	—
13	C₄×Dic₄₆	—	2	8	no	—
14	C₂₃×#95	C₂²	1	4	yes	—
15	C₂₃⋊#95	C₂²	1	4	yes	—
16	C₂₃⋊#95	C₂²	1	4	yes	—
17	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
18	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
19	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₂₃	C₂³	1	4	yes	—
21	C₂²×Dic₂₃	C₂³	1	4	yes	—
22	C₂×Dic₄₆	—	2	4	no	—
23	C₂×Dic₄₆	—	2	8	no	—
24	C₄²×C₂₃	D₄	1	4	yes	—
25	C₄²×C₂₃	Q₈	1	8	yes	complemented
26	C₄⋊Dic₂₃	—	2	4	no	—
27	C₄⋊Dic₂₃	—	2	16	no	—
28	Dic₂₃⋊C₄	—	2	8	no	—
29	C₄×Dic₂₃	—	2	8	no	—
30	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₂₃	—	2	8	no	—
32	C₂×C₄×C₂₃	—	2	4	no	—
33	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₂₃	C₂×Q₈	1	8	yes	—
36	C₂×C₄×C₂₃	C₂×Q₈	1	4	yes	—
37	C₂×Dic₂₃	—	2	4	no	—
38	C₂×Dic₂₃	—	2	4	no	—
39	C₂×Dic₂₃	—	2	4	no	—
40	C₂×Dic₂₃	—	2	8	no	—
41	C₂×Dic₂₃	#41	1	8	yes	—
42	Dic₄₆	—	2	16	no	—
43	#2399	—	23	1	no	maximal, Sylow
44	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
45	C₂²×C₂₃	C₂²×Q₈	1	2	yes	—
46	C₂²×C₂₃	C₂×#41	1	4	yes	—
47	C₄×C₂₃	—	2	4	no	—
48	C₄×C₂₃	—	2	8	no	—
49	C₄×C₂₃	C₄⋊Q₈	1	4	yes	—
50	Dic₂₃	—	2	8	no	—
51	Dic₂₃	—	4	4	no	—
52	C₂×C₄×Q₈	—	23	2	no	—
53	#398	—	23	4	no	—
54	#395	—	23	4	no	—
55	C₄×C₄⋊C₄	—	23	4	no	—
56	#376	D₂₃	1	1	yes	characteristic
57	C₂×C₂₃	#525	1	2	yes	—
58	C₂×C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
59	C₂×C₂₃	#533	1	4	yes	—
60	C₂²×Q₈	—	23	2	no	—
61	C₄×Q₈	—	46	8	no	—
62	C₂×C₄⋊C₄	—	23	4	no	—
63	C₂×C₄⋊C₄	—	23	2	no	—
64	C₂×C₄⋊C₄	—	23	8	no	—
65	C₂×C₄²	—	23	4	no	—
66	C₂×C₄²	C₂×D₂₃	1	2	yes	—
67	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
68	#95	—	23	4	no	—
69	#95	—	23	4	no	—
70	#95	C₂×D₂₃	1	4	yes	—
71	C₂₃	#2399	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	46	8	no	—
73	C₂×Q₈	—	46	4	no	—
74	C₂²×C₄	—	23	4	no	—
75	C₂²×C₄	—	23	4	no	—
76	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
77	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
78	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
79	C₄⋊C₄	—	46	16	no	—
80	C₄⋊C₄	—	46	8	no	—
81	C₄⋊C₄	—	46	4	no	—
82	C₄²	—	46	8	no	—
83	C₄²	Dic₄₆	1	8	yes	complemented
84	C₄²	D₉₂	1	4	yes	—
85	C₂³	C₂³×D₂₃	1	1	yes	characteristic
86	Q₈	—	46	16	no	—
87	C₂×C₄	—	2	8	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	23	8	no	—
90	C₂×C₄	—	46	4	no	—
91	C₂×C₄	—	46	4	no	—
92	C₂×C₄	—	46	4	no	—
93	C₂×C₄	—	46	8	no	—
94	C₂×C₄	C₂×Dic₄₆	1	8	yes	—
95	C₂×C₄	C₂×Dic₄₆	1	4	yes	—
96	C₂×C₄	C₂×D₉₂	1	4	yes	—
97	C₂×C₄	C₂×D₉₂	1	2	yes	—
98	C₂²	C₂²×Dic₄₆	1	2	yes	—
99	C₂²	C₂²×D₉₂	1	1	yes	characteristic
100	C₂²	#41×D₂₃	1	4	yes	—
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	46	8	no	—
104	C₄	—	92	4	no	—
105	C₄	#10625040	1	4	yes	—
106	C₂	#13092929	1	2	yes	—
107	C₂	C₂×#10625040	1	1	yes	characteristic
108	C₂	#13092970	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₄₆

C₂

yes

maximal

#13092349

C₂

yes

maximal

#13092338

C₂

yes

maximal

C₄×C₄⋊Dic₂₃

C₂

yes

maximal

C₂₃×#376

C₂

yes

maximal, characteristic

C₂²×Dic₄₆

C₂²

yes

—

C₂×C₄²×C₂₃

C₂²

yes

characteristic

C₂×C₄²×C₂₃

C₂²

yes

—

C₂×C₄⋊Dic₂₃

C₂²

yes

—

C₂×C₄⋊Dic₂₃

C₂²

yes

—

C₂×Dic₂₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₂₃

C₂²

yes

—

C₄×Dic₄₆

—

C₂₃×#95

C₂²

yes

—

C₂₃⋊#95

C₂²

yes

—

C₂₃⋊#95

C₂²

yes

—

C₂²×C₄×C₂₃

C₂³

yes

—

C₂²×C₄×C₂₃

C₂³

yes

—

C₂²×C₄×C₂₃

C₂³

yes

characteristic

C₂²×Dic₂₃

C₂³

yes

—

C₂²×Dic₂₃

C₂³

yes

—

C₂×Dic₄₆

—

C₂×Dic₄₆

—

C₄²×C₂₃

D₄

yes

—

C₄²×C₂₃

Q₈

yes

complemented

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

—

Dic₂₃⋊C₄

—

C₄×Dic₂₃

—

C₂³×C₂₃

C₂⁴

yes

characteristic

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₂×D₄

yes

—

C₂×C₄×C₂₃

C₂×D₄

yes

—

C₂×C₄×C₂₃

C₂×Q₈

yes

—

C₂×C₄×C₂₃

C₂×Q₈

yes

—

C₂×Dic₂₃

—

C₂×Dic₂₃

—

C₂×Dic₂₃

—

C₂×Dic₂₃

—

C₂×Dic₂₃

#41

yes

—

Dic₄₆

—

#2399

—

maximal, Sylow

C₂²×C₂₃

C₂²×D₄

yes

characteristic

C₂²×C₂₃

C₂²×Q₈

yes

—

C₂²×C₂₃

C₂×#41

yes

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

C₄⋊Q₈

yes

—

Dic₂₃

—

Dic₂₃

—

C₂×C₄×Q₈

—

#398

—

#395

—

C₄×C₄⋊C₄

—

#376

D₂₃

yes

characteristic

C₂×C₂₃

#525

yes

—

C₂×C₂₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₃

#533

yes

—

C₂²×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₃

yes

—

C₂×C₄²

C₂×D₂₃

yes

—

—

C₂×D₂₃

yes

—

C₂₃

#2399

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₃

yes

—

C₂²×C₄

C₂²×D₂₃

yes

—

C₂²×C₄

C₂²×D₂₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₄₆

yes

complemented

C₄²

D₉₂

yes

—

C₂³

C₂³×D₂₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₄₆

yes

—

C₂×C₄

C₂×Dic₄₆

yes

—

C₂×C₄

C₂×D₉₂

yes

—

C₂×C₄

C₂×D₉₂

yes

—

C₂²

C₂²×Dic₄₆

yes

—

C₂²

C₂²×D₉₂

yes

characteristic

100

C₂²

#41×D₂₃

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#10625040

yes

—

106

C₂

#13092929

yes

—

107

C₂

C₂×#10625040

yes

characteristic

108

C₂

#13092970

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₃
commutator, socle, prime radical, cosocle	C₂³×C₂₃	C₂⁴
Frattini	C₂³	C₂³×D₂₃
Fitting	C₂₃×#376	C₂
hypercenter	#376	D₂₃
hypocenter	C₂₃	#2399
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₂₃

commutator, socle, prime radical, cosocle

C₂³×C₂₃

C₂⁴

Frattini

C₂³

C₂³×D₂₃

Fitting

C₂₃×#376

C₂

D₂₃

C₂₃

G ▷ C₂³×C₂₃ ▷ C₂₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
25. C₄²×C₂₃	Q₈	semidirect
71. C₂₃	#2399	semidirect
83. C₄²	Dic₄₆	semidirect

H ≅ G/N

type

25. C₄²×C₂₃

Q₈

semidirect

71. C₂₃

#2399

semidirect

83. C₄²

Dic₄₆

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×Dic₄₆	2
#13092349	2
#13092338	2
C₄×C₄⋊Dic₂₃	2
C₂₃×#376	2
#2399	23

subgroup

index

C₂×C₄×Dic₄₆

#13092349

#13092338

C₄×C₄⋊Dic₂₃

C₂₃×#376

#2399

Subgroups — #15676690

Conjugacy classes of subgroups

Complements

Maximal subgroups